多变量公钥密码算法若干问题研究

发布时间：2018-06-03 17:01

本文选题：多变量公钥密码体制 + 非线性可逆映射　；参考：《解放军信息工程大学》2014年硕士论文

【摘要】：二十一世纪是信息的时代,继电子信息科学技术之后,量子和生物等新型信息科学正在建立和发展。量子计算机的产生将会对目前广泛使用的基于离散对数(包括椭圆曲线上的离散对数)和大数分解的公钥密码体制构成潜在的威胁。为此,基于抗量子的公钥密码体制成为密码学中一个研究的热点和重点。多变量公钥密码系统作为一种能有效抵抗未来的基于量子计算机攻击方法的密码体制,在近二十几年受到越来越多的关注。多变量公钥密码被认为是后量子时代的一种安全的密码体制的备选方案,其发展潜力不容忽视。但是,多变量公钥密码的整个体系尚未完整,随着各种攻击方法的提出,目前大部分多变量公钥密码体制均受到不同程度的攻击。因此,提出新的安全的多变量方案、对已有算法进行改进增强其性能和安全性是值得研究的课题。本文把重点放在多变量公钥密码算法的研究,主要成果如下:1.为了有效抵抗线性攻击和差分攻击,分别基于温顺变换和“特殊油醋”思想设计出两种不同的非线性可逆映射,利用扩展MQ(Multivariate Quadratic)公钥体制的思想,将上述非线性可逆映射与MI(Matsumoto-Imai)方案结合,构造出扩展多变量公钥密码算法。接着,给出扩展方案对应的加密算法和签名算法。分析结果显示:扩展多变量公钥密码算法继承了MI方案的高效性,克服了其不能抵抗线性攻击和差分攻击的缺陷,还能抵抗代数攻击。2.在基于外部干扰的MFE签名方案的基础上,设计了新的外部干扰量,提出了一种优化的基于外部干扰的签名方案。优化方案在保证安全性的同时,使得公私钥空间大大缩小;接着,针对原MFE加密方案不能抵抗高阶线性化攻击,利用上述构造的外部干扰量,重构了中心映射,提出了一种基于外部干扰的改进签名方案。改进方案保持了原MFE方案结构简单、求逆容易的性质,具有较强的安全性。3.针对油醋签名体制不能抵抗Kipnis-Shamir攻击,将基于温顺变换的非线性可逆变换和油醋签名体制结合,提出了一种改进的油醋签名方案—L-油醋方案。L-油醋方案具备很小的公私钥量,能够抵抗穷举攻击,Kipnis-Shamir攻击和代数攻击,同时,满足数字签名的基本要求。4.结合Square体制和三角型密码系统,重构了中心映射,提出了一种混合多变量公钥签名方案—Tri-Square方案。分析结果表明,Tri-Square方案克服了Square体制和三角型密码系统的缺陷,能够抵抗线性攻击,差分攻击,最小秩攻击和代数攻击。
[Abstract]:The 21 century is the era of information. After electronic information science and technology, quantum and biological new information science is being established and developed. The generation of quantum computers will pose a potential threat to the widely used public key cryptosystems based on discrete logarithms (including discrete logarithms on elliptic curves) and large number decomposition. Therefore, the anti-quantum public key cryptosystem has become a hotspot and focus in cryptography. As a kind of cryptosystem based on quantum computer attack, multivariable public key cryptosystem has attracted more and more attention in recent twenty years. Multivariable public key cryptography is considered as an alternative to secure cryptosystem in the post-quantum era, and its development potential can not be ignored. However, the whole system of multivariable public key cryptosystem is not complete. With the development of various attack methods, most multivariable public key cryptosystems are attacked to varying degrees. Therefore, it is worth studying to propose a new secure multivariable scheme and improve the performance and security of existing algorithms. This paper focuses on the research of multivariable public key cryptography algorithm, the main results are as follows: 1. In order to effectively resist linear and differential attacks, two different nonlinear reversible mappings are designed based on docile transformation and "special oil and vinegar", respectively, and the idea of extended MQ(Multivariate Quadratic public key system is used. An extended multivariable public key cryptosystem is constructed by combining the above nonlinear reversible mapping with the MIG Matsumoto-Imai) scheme. Then, the encryption algorithm and signature algorithm corresponding to the extended scheme are given. The analysis results show that the extended multivariable public key cryptosystem inherits the high efficiency of MI scheme, and overcomes the defect that it can not resist linear attack and differential attack, and can resist algebraic attack. 2. Based on the MFE signature scheme based on external interference, a new external interference scheme is designed, and an optimized signature scheme based on external interference is proposed. The optimization scheme not only ensures security, but also reduces the public and private key space greatly. Then, for the original MFE encryption scheme can not resist high-order linearization attacks, the center map is reconstructed by using the external interference of the above structure. An improved signature scheme based on external interference is proposed. The improved scheme keeps the structure of the original MFE scheme simple and easy to reverse, and has strong security. 3. In view of the fact that the oil vinegar signature scheme can not resist the Kipnis-Shamir attack, a modified oil vinegar signature scheme, -L- oil vinegar scheme. L- oil vinegar scheme has a very small amount of public and private key, which combines the nonlinear reversible transformation based on docile transformation with the oil vinegar signature scheme. It can resist the exhaustive attack Kipnis-Shamir attack and algebraic attack. At the same time, it satisfies the basic requirement of digital signature. Combined with Square system and triangular cryptosystem, a hybrid multivariable public key signature scheme, Tri-Square scheme, is proposed by reconstructing the center map. The results show that the Tri-Square scheme overcomes the defects of Square system and triangular cryptosystem, and can resist linear attack, differential attack, minimum rank attack and algebraic attack.
【学位授予单位】：解放军信息工程大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN918.1

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